Question

. Derive the formula for the kinetic
energy of an object of mass m,
moving with velocity v.​

Answer 1

Explanation:

Consider a body of mass 'm', with velocity 'v'

The kinetic energy of a body can be determined by calculating the amount of work required to move from its rest position.

w = f×s ------> eqn. 1

From Newton's second law,

f=ma---------> eqn.2

from 3rd equation of motion

v² - u² = 2as

s = (v² - u²)÷2a-------> eqn. 3

substitute the value of eqn. 2 and eqn. 3 in eqn. 1

w = (ma × v²- u²)÷ 2a

w = 1/2 m( v² - u²)--------> eqn. 4

if u=0,

from eqn. 4 w =1/2 mv²

this work done appears as the kinetic energy of the body

kinetic energy,

                        Ek=1/2mv²

Ek∝m(mass of the body)

Ek∝v²(velocity of the body)

hope this answer helps u.....